F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits
| Autor: | Louis Sharrock, Brian Coyle, Chiara Leadbeater, Marcello Benedetti |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Theoretical computer science Computer science Science QC1-999 FOS: Physical sciences generative modelling General Physics and Astronomy born machine Astrophysics Article Machine Learning (cs.LG) Quantum circuit Quadratic equation f-divergence Divergence (statistics) Quantum Physics Physics Locality local cost function Function (mathematics) Term (time) QB460-466 Quantum algorithm Quantum Physics (quant-ph) Heuristics |
| Zdroj: | Entropy; Volume 23; Issue 10; Pages: 1281 Entropy, Vol 23, Iss 1281, p 1281 (2021) Entropy |
| ISSN: | 1099-4300 |
| DOI: | 10.3390/e23101281 |
| Popis: | Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit Born machine. In particular, we consider training a quantum circuit Born machine using $f$-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any $f$-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the Born machine. The first is based on $f$-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing $f$-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback-Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another $f$-divergence, namely, the Pearson divergence. Comment: 20 pages, 9 figures, 4 tables |
| Databáze: | OpenAIRE |
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